Subgroups — D₅×Dic₅ #6035

Order 200.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₅	C₂	1	1	yes	maximal, characteristic
2	#1039	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅²	C₂²	1	1	yes	characteristic
5	C₅×D₅	C₄	1	2	yes	complemented
6	C₂×Dic₅	—	5	1	no	maximal
7	C₄×D₅	—	5	1	no	maximal
8	C₅²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
9	C₂²×C₅	—	5	1	no	—
10	C₂×D₅	D₅	1	1	yes	characteristic
11	C₄×C₅	—	5	1	no	—
12	Dic₅	—	5	1	no	—
13	Dic₅	—	5	1	no	—
14	Dic₅	—	10	2	no	—
15	Dic₅	D₅	1	1	yes	characteristic, direct product factor
16	C₂×C₅	—	2	2	no	—
17	C₂×C₅	—	5	2	no	—
18	C₂×C₅	C₂×D₅	1	1	yes	characteristic
19	C₂×C₅	C₂×D₅	1	1	yes	characteristic
20	D₅	Dic₅	1	2	yes	direct product factor
21	C₂×C₄	—	25	1	no	Sylow
22	C₅	—	2	2	no	—
23	C₅	C₄×D₅	1	1	yes	characteristic, complemented
24	C₅	C₂×Dic₅	1	1	yes	characteristic, complemented
25	C₂²	—	5	1	no	—
26	C₄	—	5	1	no	—
27	C₄	—	25	1	no	—
28	C₂	—	5	2	no	—
29	C₂	D₅²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅²
commutator, hypocenter	C₅²	C₂×C₄
Fitting, socle, cosocle	C₂×C₅²	C₂²
prime radical	C₂×C₅×D₅	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.